Note the following blurb on the Inyo National Forest website, which appears to contradict info on this page:

"Mt. Whitney Zone Day Use Quota applies for all day hikes into the Mt. Whitney Zone.
This affects all visitors that will day hike into the Mt. Whitney Zone and includes all trails, cross country travel, including the Mountaineers Route, East Face/ East Buttress and other summits within the Mt Whitney Zone. Day use of North Fork of Lone Pine Creek trail is included in the Mt. Whitney Day Use quota of 100 people each day. Visitors with an overnight permit into the Mt Whitney Zone do not require an additional day permit, the overnight permit is valid."